DLMF:28.22.E6 (Q8371)

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DLMF:28.22.E6
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    Statements

    test
    g e , 2 ⁢ m + 1 ⁢ ( h ) = ( - 1 ) m + 1 ⁢ 2 π ⁢ ce 2 ⁢ m + 1 ′ ⁡ ( 1 2 ⁢ π , h 2 ) h ⁢ A 1 2 ⁢ m + 1 ⁢ ( h 2 ) , subscript 𝑔 𝑒 2 𝑚 1 ℎ superscript 1 𝑚 1 2 𝜋 diffop Mathieu-ce 2 𝑚 1 1 1 2 𝜋 superscript ℎ 2 ℎ superscript subscript 𝐴 1 2 𝑚 1 superscript ℎ 2 {\displaystyle{\displaystyle g_{\mathit{e},2m+1}(h)=(-1)^{m+1}\sqrt{\frac{2}{% \pi}}\dfrac{\mathrm{ce}_{2m+1}'\left(\frac{1}{2}\pi,h^{2}\right)}{hA_{1}^{2m+1% }(h^{2})},}}
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    DLMF id
    DLMF:28.22.E6
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    Symbols used
    Q12283
    test
    ce n ⁡ ( z , q ) Mathieu-ce 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}
    xml-id
    C28.S2.SS6.p1.m7acdec
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    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
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    Q12284
    test
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C28.S1.XMD1.m1edec
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    Q12294
    test
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C28.S1.XMD11.m1edec
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    Q12302
    test
    g e , n ⁢ ( h ) subscript 𝑔 𝑒 𝑛 ℎ {\displaystyle{\displaystyle g_{\mathit{e},n}(h)}}
    xml-id
    C28.S22.XMD1.m1edec
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    Q12287
    test
    A m ⁢ ( q ) subscript 𝐴 𝑚 𝑞 {\displaystyle{\displaystyle A_{m}(q)}}
    xml-id
    C28.S4.XMD1.m1adec
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